Airflow is relevant in closed cases because without proper airflow, the warm air will stay trapped inside the case and heat up the components. Since the Core P3 is open, you will be fine with air coolers if you don't go crazy on the overclocking. The hot air can still escape.
Installing fans where the radiator would usually go really only make sense if you want to cool your hidden hard drives or for aesthetical reasons. If you've got the fans anyway and will mount them onto the radiator when you put in the water cooling, go for it. If you don't install extra fans, that is no big deal either.

We are providing some of the dimensions in the first post of this thread here: http://community.thermaltake.com/index.php?/topic/1092-core-x-series/
The left side is designated for the PSU but you can change that and install the PSU on the right side. That leaves you with around 150mm of space for your radiator and fans.
You will need to think about HDD placement, though.
The front fits two 120mm fans without losing a 5.25" bay but for a 240mm radiator you would probably have to remove the bottom 5.25" bay to make it fit.

The beauty about the kits is that you can expand however you wish and add more or different components to your loop. For the hard tubes, you will require different fittings so you'd have to acquire those as well. The soft tube compressions are not compatible with hard tubes.

Hello,
you can find Thermaltake products at most major etailers, like SCAN, box, Eclipse, CCL, Chillblast, FiercePC, AriaPC and many more. When it comes to the water cooling parts, you are somewhat more limited. I would recommend checking out SCAN, box or watercooling.co.uk for that. We are working on bringing better availability of the Pacific water cooling products to the European market. Thanks for your interest in our products!

You can use air coolers with a height of up to 160mm (which applies to most tower coolers with a 140mm fan), the maximum GPU length is 390mm if you take out the front fan and 365mm with a front fan (for reference: A GTX1080 has around 270mm).
You should be absolutely golden for future upgrades. Just make sure to pick a motherboard that allows easy upgrades along the line (has extra RAM slots, free SATA connectors, enough PCIe slots and supports entry level and high end CPUs). Power will become less and less of an issue since the most power hungry components are becoming more and more efficient. 500-600W should be enough, even for an ambitious and powerful system.
The Versa C21 comes with a preinstalled exhaust fan in the rear. Depending on your setup, you might want to add a few more fans in the front and/or top. However, you can just test out how the temperatures are with the basic setup and add more fans if the temperatures are too high. They are easy to upgrade without dismantling the whole PC. This case is perfectly capable of creating a great airflow for air cooling and does not require water cooling. We put that in to demonstrate what the chassis is capable of and because it looks better.

The Core P3 will fit your GPU, just be aware it might stick out a bit and cover the area in front of the radiator a little bit (by about 2cm). This is important because it might collide with the reservoir but it should probably fit. However, it might become difficult when you go SLI. Below you'll find a photo of the Core P3 with the Strix 980Ti (30.5cm)

The Riing fans are geared towards static pressure and radiators but are perfectly fine as case fans too.
The single-colour Riing fans have a 3pin connector (and a low noise cable). The Riing RGB fans have a 4pin connector and support PWM.
In a few weeks, we will release the Riing RGB TT Premium edition, which is a software-controlled Riing RGB fan with fan blades that are optimized for air flow, however. They will perform better as case fans that the Riing fans that are currently available.

The Core X71 only supports 1x 360mm radiator at the top.
How are you using the bottom compartment? Have you tried installing the power supply or radiator in there to free up space around the motherboard?